Crack-front instability in a confined elastic film

2006 ◽  
Vol 462 (2075) ◽  
pp. 3233-3251 ◽  
Author(s):  
M Adda-Bedia ◽  
L Mahadevan
Keyword(s):  
Stability Analysis ◽  
Film Thickness ◽  
Elastic Plate ◽  
Linear Stability Analysis ◽  
Crack Front ◽  
Length Scales ◽  
Adhesive Film ◽  
Straight Crack ◽  
Multiple Length Scales ◽  
Elastic Film

We study the undulatory instability of a straight crack front generated by peeling a flexible elastic plate from a thin elastomeric adhesive film. We show that there is a threshold for the onset of the instability that is dependent on the ratio of two length-scales that arise naturally in the problem: the thickness of the film and an elastic length defined by the stiffness of the plate and that of the film. A linear stability analysis predicts that the wavelength of the instability scales linearly with the film thickness. Our results are qualitatively and quantitatively consistent with recent experiments, and show how crack fronts may lose stability due to a competition between bulk and surface effects in the presence of multiple length scales.

scholarly journals A Comprehensive Model to Predict Simplex Atomizer Performance

1998 ◽  
Author(s):  
Y. Liao ◽  
A. T. Sakman ◽  
S. M. Jeng ◽  
M. A. Jog ◽  
M. Benjamin
Keyword(s):  
Stability Analysis ◽  
Film Thickness ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Liquid Fuel ◽  
Density Ratio ◽  
Liquid Sheet ◽  
Unstable Wave ◽  
Liquid Sheets ◽  
Breakup Model

The performance of liquid fuel atomizer has direct effects on combustion efficiency, pollutant emission and stability. Pressure swirl atomizer, or simplex atomizer, is widely used in liquid fuel combustion devices in aircraft and power generation industry. A computational, experimental, and theoretical study is conducted to predict its performance. The Arbitrary-Lagrangian-Eulerian method with finite volume scheme is employed in the CFD model. Internal flow characteristics of the simplex atomizer as well as its performance parameters such as discharge coefficient, spray angle and film thickness are predicted. A temporal linear stability analysis is performed for cylindrical liquid sheets under 3-D disturbance. The model incorporates swirling velocity component, finite film thickness and radius which are essential features of conical liquid sheets emanating from simplex atomizers. It is observed that the relative velocity between liquid and gas phase, density ratio and surface curvature enhance the interfacial aerodynamic instability. As Weber number and density ratio increase, both the wave growth rate and the unstable wave number range increase. Combination of axial and swirling velocity components is more effective than single axial component for disintegration of liquid sheet. A breakup model for conical liquid sheet is proposed. Combining the breakup model with linear stability analysis, mean drop sizes are predicted. The theoretical results are compared with measurement data and agreement is very good.

scholarly journals Stability of a composite thick plate with an inhomogeneous field of initial stresses

2018 ◽  
Vol 226 ◽  
pp. 01013
Author(s):  
Vadim V. Eremeev ◽  
Natalia Y. Shubchinskaya ◽  
Denis V. Ivashchenko ◽  
Vsevolod A. Minko
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Linear Stability ◽  
Nonlinear Elasticity ◽  
Elastic Plate ◽  
Linear Stability Analysis ◽  
Thick Plate ◽  
Boundary Value ◽  
Initial Stresses ◽  
Inhomogeneous Field

We discuss the linear stability analysis for a rectangular twolayered elastic plate. Each layer of the plate was obtained due to inflation of an annular wedge of a cylinder. As a result, in the plate there are initial stresses. The main aim of the paper is to analyse the influence of the initial stresses on the buckling. Here we use the 3D nonlinear elasticity technique. The linearized boundary-value problem is derived and its non-trivial solutions were obtained.

scholarly journals A Comprehensive Model to Predict Simplex Atomizer Performance

1999 ◽  
Vol 121 (2) ◽  
pp. 285-294 ◽  
Author(s):  
Y. Liao ◽  
A. T. Sakman ◽  
S. M. Jeng ◽  
M. A. Jog ◽  
M. A. Benjamin
Keyword(s):  
Stability Analysis ◽  
Film Thickness ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Density Ratio ◽  
Spray Angle ◽  
Small Scale ◽  
Finite Volume Scheme ◽  
Axial Component ◽  
Liquid Sheets

The pressure swirl atomizer, or simplex atomizer, is widely used in liquid fuel combustion devices in the aerospace and power generation industries. A computational, experimental, and theoretical study was conducted to predict its performance. The Arbitrary-Lagrangian-Eulerian method with a finite-volume scheme is employed in the CFD model. Internal flow characteristics of the simplex atomizer, as well as its performance parameters such as discharge coefficient, spray angle and film thickness, are predicted. A temporal linear stability analysis is performed for cylindrical liquid sheets under three-dimensional disturbances. The model incorporates the swirling velocity component, finite film thickness and radius that are essential features of conical liquid sheets emanating from simplex atomizers. It is observed that the relative velocity between the liquid and gas phases, density ratio and surface curvature enhance the interfacial aerodynamic instability. The combination of axial and swirling velocity components is more effective than only the axial component for disintegration of liquid sheet. For both large and small-scale fuel nozzles, mean droplet sizes are predicted based on the linear stability analysis and the proposed breakup model. The predictions agree well with experimental data at both large and small scale.

Buckling Instability of Straight Edge Cracks

1995 ◽  
Vol 62 (3) ◽  
pp. 620-625 ◽  
Author(s):  
H. M. Jensen ◽  
M. D. Thouless
Keyword(s):  
Crack Growth ◽  
Crack Front ◽  
Driving Force ◽  
Edge Crack ◽  
Straight Edge ◽  
Straight Crack ◽  
Crack Driving Force ◽  
Buckling Instability ◽  
Elastic Film ◽  
Edge Cracks

A buckling instability in a system where a straight edge crack lies at the interface between a thin elastic film and a substrate is analysed theoretically and experimentally. The buckling, which can occur also under remote tensile loads, may result in crack growth before the conventional criterion for fracture is met on the straight crack front by enhancing the mode adjusted crack driving force. If crack growth occurs, buckling will cause a wavy crack front to develop.

Power Flux along a Straight Crack in an Elastic Plate

2001 ◽  
Vol 47 (3) ◽  
pp. 243
Author(s):  
I. V. Andronov
Keyword(s):  
Elastic Plate ◽  
Power Flux ◽  
Straight Crack
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